An innovative meshless approach for solving 2D Allen-Cahn equations using the RBF-compact finite difference method. [PDF]
Sci RepFardi M, Azarnavid B, Emami H.
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Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT In this paper we study the long‐time stability of the Cauchy one‐leg θ$$ \theta $$‐methods for the two‐dimensional Navier‐Stokes equations. We establish the uniform dissipativity in H1$$ {H}^1 $$, in the sense that the semi‐discrete‐in‐time approximations possess a global attractor for a small enough time step, using the discrete Grönwall ...
Isabel Barrio Sanchez +2 more
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Stability and Robustness of Time-discretization Schemes for the Allen-Cahn Equation via Bifurcation and Perturbation Analysis. [PDF]
J Comput PhysHao W, Lee S, Xu X, Xu Z.
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Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.ABSTRACT To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of
Andres Ortegón‐Villacorte +1 more
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A replicator model with transport dynamics on networks for species evolution. [PDF]
J Math BiolCoclite A +3 more
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Learning Differential Equations From Numerically Integrated Artificial Neural Networks
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.ABSTRACT For numerical investigation of dynamical systems, the formulation of the corresponding ordinary differential equations (ODE) based on physical principles is usually the first and most crucial step. However, if the underlying physics is not fully understood or the required expert knowledge for modeling is missing, setting up these differential ...
Timo Bielitz, Dieter Bestle
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Deterministic, stochastic, and mean-field PDE models in neuroscience. [PDF]
Front Comput NeurosciÇetin C +5 more
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Redefining Optimal Coverage Path Planning for FLS‐Equipped AUVs With Deep Reinforcement Learning
Journal of Field Robotics, Volume 43, Issue 6, Page 3617-3632, September 2026.ABSTRACT Autonomous Underwater Vehicles (AUVs) have emerged as indispensable tools for a variety of subsea tasks, from habitat monitoring and seabed mapping to infrastructure inspection and mine countermeasures. A fundamental challenge in this field is Coverage Path Planning (CPP), the problem of ensuring complete and efficient area coverage.
Lorenzo Cecchi +3 more
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A novel exponential tension field for salt-and-pepper image denoising. [PDF]
Sci RepKazemi Torbaghan SM +3 more
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Exploring the Use and Impact of Composite Materials in Robotics: A Systematic Review
Journal of Field Robotics, Volume 43, Issue 6, Page 4037-4060, September 2026.ABSTRACT Lightweight and high‐strength materials are important in robotics, as structural design impacts efficiency, payload capacity, and energy consumption. Composite materials, with their superior stiffness‐to‐weight ratios and multifunctional properties, offer clear advantages over conventional metals and polymers.
Doglas Negri +4 more
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